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Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport

AUTHORS

Christoph Lehrenfeld, Arnold Reusken

ABSTRACT

We consider a standard sharp interface model for the fluid dynamics in a two-
phase incompressible flow, combined with a convection-diffusion model for solute transport. Some
important numerical challenges related to these models are discussed. We present a finite element
discretization method for the solute transport model. The method is based on an Eulerian approach,
i.e. computational grids are not aligned to the interface and do not follow the interface motion. The
interface motion is described using the level-set technique. We treat three numerical techniques,
namely the extended finite element method (XFEM) for the approximation of discontinuities, the
Nitsche-method for a convenient handling of interface conditions (e.g., Henry condition) and the
space-time finite element technique. The basic underlying ideas are explained. These techniques
are combined and result in the space-time Nitsche-XFEM that is used for the discretization of two-phase solute transport problem. Properties of this method are discussed. Results of numerical
experiments with this method are presented.